Advanced Lane Finding

The goals / steps of this project are the following:

  • Compute the camera calibration matrix and distortion coefficients given a set of chessboard images.
  • Apply a distortion correction to raw images.
  • Use color transforms, gradients, etc., to create a thresholded binary image.
  • Apply a perspective transform to rectify binary image ("birds-eye view").
  • Detect lane pixels and fit to find the lane boundary.
  • Determine the curvature of the lane and vehicle position with respect to center.
  • Warp the detected lane boundaries back onto the original image.
  • Output visual display of the lane boundaries and numerical estimation of lane curvature and vehicle position.

Imports

In [1]:
import numpy as np
import cv2
import glob
import pickle
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
%matplotlib inline

1. Computing the Camera Calibration Using Chessboard Images

In [2]:
# Prepare object points
objp = np.zeros((6*9,3), np.float32)
objp[:,:2] = np.mgrid[0:9,0:6].T.reshape(-1,2)

# Arrays to store object points and image points from all the images.
objpoints = [] # 3d points in real world space
imgpoints = [] # 2d points in image plane.

# Make a list of calibration images
images = glob.glob('./camera_cal/calibration*.jpg')

fig,axs = plt.subplots(10, 2, figsize=(40,100))
axs = axs.ravel()

# Step through the list and search for chessboard corners
for i, fname in enumerate(images):
    img = cv2.imread(fname)
    gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)

    # Find the chessboard corners
    ret, corners = cv2.findChessboardCorners(gray, (9,6),None)

    # If found, add object points, image points
    if ret == True:
        objpoints.append(objp)
        imgpoints.append(corners)

        # Draw and display the corners
        img = cv2.drawChessboardCorners(img, (9,6), corners, ret)
        axs[i].imshow(img)
        

Calculate Camera Distortion

In [3]:
# Calculate camera matrix and distortion coefficients
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, img.shape[1:], None, None)

# Save camera paramters
dist_pickle = {}
dist_pickle["mtx"] = mtx
dist_pickle["dist"] = dist
pickle.dump( dist_pickle, open( "calibration.p", "wb" ) )

2. Applying Distortion Correction

In [4]:
# Read in an image
img = cv2.imread('./camera_cal/calibration1.jpg')

def cal_undistort(img, objpoints, imgpoints):
    """
    Take an image, object points, and image points
    Perform camera calibration and image distortion correction
    Return the undistorted image
    """ 
    ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, img.shape[1:], None, None)
    undist = cv2.undistort(img, mtx, dist, None, mtx)
    return undist

undistorted = cal_undistort(img, objpoints, imgpoints)

f, (ax1, ax2) = plt.subplots(1, 2, figsize=(24, 9))
f.tight_layout()
ax1.imshow(img)
ax1.set_title('Original Image', fontsize=50)
ax2.imshow(undistorted)
ax2.set_title('Undistorted Image', fontsize=50)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)

plt.savefig('./output_images/undistort_output.jpg')

3. Apply Perspective Transform

In [5]:
def corners_unwarp(img, nx, ny, mtx, dist, draw_corners_flag):
    """
    Take an image and do the following steps:
     1) Undistort using mtx and dist
     2) Convert to grayscale
     3) Find the chessboard corners
     4) If corners found: 
             a) draw corners
             b) define 4 source points src = np.float32([[,],[,],[,],[,]])
                 Note: you could pick any four of the detected corners 
                  as long as those four corners define a rectangle
             c) define 4 destination points dst = np.float32([[,],[,],[,],[,]])
             d) use cv2.getPerspectiveTransform() to get M, the transform matrix
             e) use cv2.warpPerspective() to warp your image to a top-down view
    
    Return the warped image and perspective transform matrix M
    """     

    # Remove distortion
    undist = cv2.undistort(img, mtx, dist, None, mtx)
    
    # Convert to grayscale
    gray = cv2.cvtColor(undist, cv2.COLOR_BGR2GRAY)
    
    # Search for corners
    ret, corners = cv2.findChessboardCorners(gray, (nx, ny), None)

    M = []
    warped = []
    
    if ret == True:

        # If we found corners, draw them
        if draw_corners_flag:
            cv2.drawChessboardCorners(undist, (nx, ny), corners, ret)
        
        # Choose offset (for dst points) from image corners for plotting purposes
        offset = 100 
        
        # Grab the image shape
        img_size = (gray.shape[1], gray.shape[0])

        # Grab the outer four detected corners for source points
        src = np.float32([corners[0], corners[nx-1], corners[-1], corners[-nx]])
        
        # Choose points for destination points (for displaying our warped result)
        dst = np.float32([[offset, offset], [img_size[0]-offset, offset], 
                                     [img_size[0]-offset, img_size[1]-offset], 
                                     [offset, img_size[1]-offset]])

        
        warped, M, Minv = unwarp(img, src, dst)
  
    return warped, M


def unwarp(img, src, dst):
    """
    Take an image and unwarp it. 
    Return the warped image, the transform matrix M, and the inverse Minv
    """
    # Grab the image shape
    img_size = (img.shape[1], img.shape[0])

    # Given src and dst points, calculate the perspective transform matrix
    M = cv2.getPerspectiveTransform(src, dst)
    Minv = cv2.getPerspectiveTransform(dst, src)

    # Warp the image using OpenCV warpPerspective()
    warped = cv2.warpPerspective(img, M, img_size)

    return warped, M, Minv

Test: Chessboard

In [6]:
images = glob.glob('./camera_cal/calibration*.jpg')

nx = 9 # the number of inside corners in x
ny = 6 # the number of inside corners in y

# Step through the list and search for chessboard corners
for fname in images:

    # Read an image
    img = cv2.imread(fname)
    
    # Warp the image
    warped, perspective_M = corners_unwarp(img, nx, ny, mtx, dist, False)

    if warped != []:
        f, (ax1, ax2) = plt.subplots(1, 2, figsize=(20, 10))
        ax1.imshow(img)
        ax1.set_title('Original Image', fontsize=30)
        ax2.imshow(warped)
        ax2.set_title('Undistorted and Warped Image', fontsize=30)
/Users/kamiarkordari/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:15: DeprecationWarning: elementwise comparison failed; this will raise an error in the future.
  from ipykernel import kernelapp as app

Straight Street Lines

In [7]:
# Plot and save output images 
def plot_save_two_images(img1, img2, title1, title2, filename):
    # Plot the result
    f, (ax1, ax2) = plt.subplots(1, 2, figsize=(20, 10))
    f.tight_layout()
    ax1.imshow(img1)
    ax1.set_title(title1, fontsize=30)
    ax2.imshow(img2, cmap='gray')
    ax2.set_title(title2, fontsize=30)
    plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
    plt.savefig(filename)
In [8]:
# Read the image
img = cv2.imread('./test_images/straight_lines1.jpg')
img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)

# Undistort the image
undist = cv2.undistort(img, mtx, dist, None, mtx)
undist_copy = undist.copy()

# Pick four source points
left_bottom = (185, 720)
left_top = (585, 455)
right_bottom = (1125, 720)
right_top = (695, 455)

src = np.float32([left_top, right_top, right_bottom, left_bottom])

# Pick four destination points
offset = 200
height, width, _ = img.shape
dst = np.float32([(offset, 0), (width-offset, 0), (width-offset, height), (offset, height)])

# Unwarp the image
top_down, M, Minv = unwarp(undist, src, dst)

# Plot results
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(20, 10))
ax1.imshow(img)
ax1.set_title('Original Image', fontsize=30)
ax2.imshow(undist)
ax2.set_title('Undistorted Image', fontsize=30)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)    

plt.savefig('./output_images/straight_lines1_undistort_output.jpg')

cv2.line(top_down, (offset, 0), (offset, height), [255, 0, 0], 4)
cv2.line(top_down, (offset, 0), (width-offset, 0), [255, 0, 0], 4)
cv2.line(top_down, (width-offset, 0), (width-offset, height), [255, 0, 0], 4)
cv2.line(top_down, (width-offset, height), (offset, height), [255, 0, 0], 4)

fname = './test_images/straight_lines1.jpg'    
fdir = './output_images/'
plot_save_two_images(img, top_down, 'Original Image', 'Perspective Transformed', fdir+'straight_lines1_perspective_transform_output.jpg')

4. Using Color Transforms, Gradients, etc., to Create a Thresholded Binary Image

The goal is to identify pixels where the gradient of an image falls within a specified threshold range.

Sobel Gradient

In [9]:
def abs_sobel_thresh(img, orient='x', sobel_kernel=3, thresh=(0, 255)):
    """
    Take an image, gradient orientation, and threshold min / max values.
    Apply Sobel.  
    Return a binary image. 
    """
    
    # Convert to grayscale
    gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
    
    # Apply x or y gradient with the OpenCV Sobel() function
    # and take the absolute value
    if orient == 'x':
        abs_sobel = np.absolute(cv2.Sobel(gray, cv2.CV_64F, 1, 0, ksize=sobel_kernel))
    if orient == 'y':
        abs_sobel = np.absolute(cv2.Sobel(gray, cv2.CV_64F, 0, 1, ksize=sobel_kernel))
    
    # Rescale back to 8 bit integer
    scaled_sobel = np.uint8(255*abs_sobel/np.max(abs_sobel))
    
    # Create a copy and apply the threshold
    binary_output = np.zeros_like(scaled_sobel)
    
    # Apply thresholds
    binary_output[(scaled_sobel >= thresh[0]) & (scaled_sobel <= thresh[1])] = 1

    # Return the result
    return binary_output

Magnitude of the Gradient

In [10]:
def mag_thresh(img, sobel_kernel=3, thresh=(0, 255)):
    """
    Take an image, sobel kernel size, and threshold values
    Apply thresholds on magnitude of Sobel gradients
    Return the binary image.
    """
    
    # Convert to grayscale
    gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
    
    # Take both Sobel x and y gradients
    sobelx = cv2.Sobel(gray, cv2.CV_64F, 1, 0, ksize=sobel_kernel)
    sobely = cv2.Sobel(gray, cv2.CV_64F, 0, 1, ksize=sobel_kernel)
    
    # Calculate the gradient magnitude
    gradmag = np.sqrt(sobelx**2 + sobely**2)
    
    # Rescale to 8 bit
    scale_factor = np.max(gradmag)/255 
    gradmag = (gradmag/scale_factor).astype(np.uint8) 
    
    # Create a binary image of ones where threshold is met, zeros otherwise
    binary_output = np.zeros_like(gradmag)
    binary_output[(gradmag >= thresh[0]) & (gradmag <= thresh[1])] = 1

    # Return the binary image
    return binary_output

Direction of the Gradient

In [11]:
def dir_threshold(img, sobel_kernel=3, thresh=(0, np.pi/2)):
    """
    Take an image, sobel kernel size, and threshold values
    Apply thresholds on direction of Sobel gradients
    Return the binary image.
    """

    # Grayscale
    gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
    
    # Calculate the x and y gradients
    sobelx = cv2.Sobel(gray, cv2.CV_64F, 1, 0, ksize=sobel_kernel)
    sobely = cv2.Sobel(gray, cv2.CV_64F, 0, 1, ksize=sobel_kernel)
    
    # Take the absolute value of the gradient direction, 
    # apply a threshold, and create a binary image result
    absgraddir = np.arctan2(np.absolute(sobely), np.absolute(sobelx))
    binary_output =  np.zeros_like(absgraddir)
    binary_output[(absgraddir >= thresh[0]) & (absgraddir <= thresh[1])] = 1

    # Return the binary image
    return binary_output

Combining Thresholds

In [12]:
# Read the test images
images = glob.glob('./test_images/*.jpg')

# Sobel kernel size
ksize = 3 

# Step through the images and apply thresholding
for fname in images:

    img = cv2.imread(fname)
    img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)

    # Apply each of the thresholding functions
    gradx = abs_sobel_thresh(img, orient='x', sobel_kernel=ksize, thresh=(10, 100))
    grady = abs_sobel_thresh(img, orient='y', sobel_kernel=ksize, thresh=(10, 100))
    mag_binary = mag_thresh(img, sobel_kernel=ksize, thresh=(50, 150))
    dir_binary = dir_threshold(img, sobel_kernel=ksize, thresh=(.7, 1))

    # Combine thresholds
    combined = np.zeros_like(dir_binary)
    combined[((gradx == 1) & (grady == 1)) | ((mag_binary == 1) & (dir_binary == 1))] = 1

    # Plot the result
    f, (ax1, ax2, ax3, ax4, ax5, ax6) = plt.subplots(1, 6, figsize=(20, 10))
    f.tight_layout()
    ax1.imshow(img)
    ax1.set_title('Original', fontsize=20)
    ax2.imshow(gradx, cmap='gray')
    ax2.set_title('X Gradient', fontsize=20)
    ax3.imshow(grady, cmap='gray')
    ax3.set_title('Y Gradient', fontsize=20)
    ax4.imshow(mag_binary, cmap='gray')
    ax4.set_title('Magnitude', fontsize=20)
    ax5.imshow(dir_binary, cmap='gray')
    ax5.set_title('Direction', fontsize=20)
    ax6.imshow(combined, cmap='gray')
    ax6.set_title('Combined', fontsize=20)
    plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
    

HLS and Color Thresholds

In [13]:
def hls_select(img, thresh=(0, 255)):
    """
    Take an image and threshold values
    Threshold the S-channel of HLS
    Return the binary image
    """    

    hls = cv2.cvtColor(img, cv2.COLOR_RGB2HLS)
    s_channel = hls[:,:,2]
    binary_output = np.zeros_like(s_channel)
    binary_output[(s_channel > thresh[0]) & (s_channel <= thresh[1])] = 1
    return binary_output

Combine Color and Gradient

In [14]:
def thresholding_pipeline_hyper_parameters(image, s_thresh=(0, 255), 
                          sx_thresh=(0, 255), 
                          sy_thresh=(0,255), 
                          smag_thresh=(0, 255), 
                          sdir_thresh= (0,1.5), 
                          s_flag=False, sx_flag=False, sy_flag=False, smag_flag=False, sdir_flag=False):
    """
    Take an image and threshold values
    Combine thresholding of the S-channel of HLS and X gradient with Sobel
    Return the combines binary image
    """
    img = np.copy(image)
    
    # Sobel X gradient
    gradx_binary = abs_sobel_thresh(img, orient='x', thresh=sx_thresh)

    # Sobel Y gradient
    grady_binary = abs_sobel_thresh(img, orient='y', thresh=sy_thresh)

    # Sobel gradient magnitude
    mag_binary = mag_thresh(img, sobel_kernel=3, thresh=smag_thresh)

    # Gradient direction
    dir_binary = dir_threshold(img, sobel_kernel=15, thresh=sdir_thresh)

    # S-channel thresholding
    s_binary = hls_select(img, thresh=s_thresh)
    
    # Combine the two binary thresholds
    combined_binary = np.zeros_like(gradx_binary)
    combined_binary[((s_binary == 1) & s_flag) 
                    | ((gradx_binary == 1) & sx_flag)
                    | ((grady_binary == 1) & sy_flag)
                    | ((mag_binary == 1) & smag_flag)
                    | ((dir_binary == 1) & sdir_flag)] = 1

    return combined_binary

Selecting Thresholding Hyperparameters

In [15]:
fname = './test_images/straight_lines1.jpg'    
fdir = './output_images/'

img = cv2.imread(fname)
img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)

# Run the thresholding function
# Sobel X gradient
gradx_binary = thresholding_pipeline_hyper_parameters(img, sx_thresh=(10, 100), sx_flag=True)
plot_save_two_images(img, gradx_binary, 'Original Image', 'Gradient X', fdir+'straight_lines1_sobel_x.jpg')

# Sobel Y gradient
grady_binary = thresholding_pipeline_hyper_parameters(img, sy_thresh=(20, 100), sy_flag=True)
plot_save_two_images(img, grady_binary, 'Original Image', 'Gradient Y', fdir+'straight_lines1_sobel_y.jpg')

# Sobel gradient magnitude
mag_binary = thresholding_pipeline_hyper_parameters(img, smag_thresh=(30, 100), smag_flag=True)
plot_save_two_images(img, mag_binary, 'Original Image', 'Magnitude', fdir+'straight_lines1_sobel_magnitude.jpg')

# Gradient direction
dir_binary = thresholding_pipeline_hyper_parameters(img, sdir_thresh=(0.8, 1.2), sdir_flag=True)
plot_save_two_images(img, dir_binary, 'Original Image', 'Direction', fdir+'straight_lines1_sobel_direction.jpg')

# S-channel thresholding
hls_binary = thresholding_pipeline_hyper_parameters(img, s_thresh=(90, 255), s_flag=True)
plot_save_two_images(img, hls_binary, 'Original Image', 'S Channel', fdir+'straight_lines1_hls.jpg')

# Combined result
combined_binary = thresholding_pipeline_hyper_parameters(img, 
                                        s_thresh=(170, 255), 
                                        sx_thresh=(20, 100), 
                                        sy_thresh=(20,100), 
                                        smag_thresh=(20, 100), 
                                        sdir_thresh= (0.8,1.2), 
                                        s_flag=True, sx_flag=True, sy_flag=False, smag_flag=False, sdir_flag=False)
plot_save_two_images(img, combined_binary, 'Original Image', 'Combined', fdir+'straight_lines1_thresholding_output.jpg')

Final Thresholding Pipeline

In [16]:
def thresholding_pipeline(image, s_thresh=(170, 255), sx_thresh=(20, 100)):
    """
    Take an image and threshold values
    Combine thresholding of the S-channel of HLS and X gradient with Sobel
    Return the combines binary image
    """

    img = np.copy(image)
    
    # Convert to HLS color space and separate the V channel
    hls = cv2.cvtColor(img, cv2.COLOR_RGB2HLS)
    l_channel = hls[:,:,1]
    s_channel = hls[:,:,2]
    
    # Sobel x
    sobelx = cv2.Sobel(l_channel, cv2.CV_64F, 1, 0) 
    abs_sobelx = np.absolute(sobelx) 
    scaled_sobel = np.uint8(255*abs_sobelx/np.max(abs_sobelx))
    
    # Threshold x gradient
    sxbinary = np.zeros_like(scaled_sobel)
    sxbinary[(scaled_sobel >= sx_thresh[0]) & (scaled_sobel <= sx_thresh[1])] = 1
    
    # Threshold color channel
    s_binary = np.zeros_like(s_channel)
    s_binary[(s_channel >= s_thresh[0]) & (s_channel <= s_thresh[1])] = 1
        
    # Combine the two binary thresholds
    combined_binary = np.zeros_like(sxbinary)
    combined_binary[(s_binary == 1) | (sxbinary == 1)] = 1

    return combined_binary
In [17]:
# Test thresholding pipline for all test images
images = glob.glob('./test_images/*.jpg')

test_images = []

# Step through the images
for fname in images:

    # Read the image
    img = cv2.imread(fname)
    img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)

    # Undistort the image
    undist = cv2.undistort(img, mtx, dist, None, mtx)
    undist_copy = undist.copy()

    # Threshold
    binary_image = thresholding_pipeline(undist)
        
    # Pick four source points
    left_bottom = (185, 720)
    left_top = (585, 455)
    right_bottom = (1125, 720)
    right_top = (695, 455)
    src = np.float32([left_top, right_top, right_bottom, left_bottom])

    # Pick four destination points
    offset = 200
    height, width = binary_image.shape
    dst = np.float32([(offset, 0), (width-offset, 0), (width-offset, height), (offset, height)])

    # Unwarp the image
    top_down, M, Minv = unwarp(binary_image, src, dst)
    
    # Plot results
    fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(40, 20))
    ax1.imshow(undist_copy)
    ax1.set_title('Original Image', fontsize=30)
    ax2.imshow(binary_image)
    ax2.set_title('Thresholded', fontsize=30)
    ax3.imshow(top_down)
    ax3.set_title('Top Down', fontsize=30)

    test_images.append({'file':fname, 'image':img, 'threshold':binary_image, 'top_down': top_down})
    
In [18]:
# Saving sample results to show in README.md 
fname = './test_images/straight_lines1.jpg'    
fdir = './output_images/'
plot_save_two_images(test_images[7]['image'], test_images[7]['top_down'], 'Original Image', 'Thresholding + Perspective Transform', fdir+'straight_lines1_top_down_output.jpg')

5. Locate the Lane Lines

In [19]:
def hist(img):
    
    # Grab only the bottom half of the image. Lane lines are likely to be mostly vertical nearest to the car.
    bottom_half = img[img.shape[0]//2:,:]

    # Sum across image pixels vertically
    histogram = np.sum(bottom_half, axis=0)
    
    return histogram
In [20]:
# Step through the images
for image_index in test_images:

    # Normalize the image
    img = image_index['top_down']/255
 
    # Create histogram of image binary activations
    histogram = hist(img)

    # Visualize the resulting histogram
    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(40, 20))
    ax1.imshow(image_index['top_down'])
    ax1.set_title('Top Down', fontsize=30)
    ax2.plot(histogram)
    ax2.set_title('Histogram', fontsize=30)

Implement Sliding Windows and Fit a Polynomial

In [21]:
def find_lane_pixels(binary_warped):
    
    # Take a histogram of the bottom half of the image
    histogram = np.sum(binary_warped[binary_warped.shape[0]//2:,:], axis=0)
    
    # Create an output image to draw on and visualize the result
    out_img = np.dstack((binary_warped, binary_warped, binary_warped))
    
    # Find the peak of the left and right halves of the histogram
    # These will be the starting point for the left and right lines
    midpoint = np.int(histogram.shape[0]//2)
    leftx_base = np.argmax(histogram[:midpoint])
    rightx_base = np.argmax(histogram[midpoint:]) + midpoint

    leftx_base = np.argmax(histogram[:midpoint])
    rightx_base = np.argmax(histogram[midpoint:]) + midpoint

    # HYPERPARAMETERS
    # Choose the number of sliding windows
    nwindows = 9
    # Set the width of the windows +/- margin
    margin = 150
    # Set minimum number of pixels found to recenter window
    minpix = 50

    # Set height of windows - based on nwindows above and image shape
    window_height = np.int(binary_warped.shape[0]//nwindows)
    
    # Identify the x and y positions of all nonzero pixels in the image
    nonzero = binary_warped.nonzero()
    nonzeroy = np.array(nonzero[0])
    nonzerox = np.array(nonzero[1])
    
    # Current positions to be updated later for each window in nwindows
    leftx_current = leftx_base
    rightx_current = rightx_base

    # Create empty lists to receive left and right lane pixel indices
    left_lane_inds = []
    right_lane_inds = []

    # Step through the windows one by one
    for window in range(nwindows):
        # Identify window boundaries in x and y (and right and left)
        win_y_low = binary_warped.shape[0] - (window+1)*window_height
        win_y_high = binary_warped.shape[0] - window*window_height
        win_xleft_low = leftx_current - margin
        win_xleft_high = leftx_current + margin
        win_xright_low = rightx_current - margin
        win_xright_high = rightx_current + margin
        
        # Draw the windows on the visualization image
        cv2.rectangle(out_img,(win_xleft_low,win_y_low),
        (win_xleft_high,win_y_high),(0,255,0), 2) 
        cv2.rectangle(out_img,(win_xright_low,win_y_low),
        (win_xright_high,win_y_high),(0,255,0), 2) 
        
        # Identify the nonzero pixels in x and y within the window #
        good_left_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & 
        (nonzerox >= win_xleft_low) &  (nonzerox < win_xleft_high)).nonzero()[0]
        good_right_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & 
        (nonzerox >= win_xright_low) &  (nonzerox < win_xright_high)).nonzero()[0]
        
        # Append these indices to the lists
        left_lane_inds.append(good_left_inds)
        right_lane_inds.append(good_right_inds)
        
        # If you found > minpix pixels, recenter next window on their mean position
        if len(good_left_inds) > minpix:
            leftx_current = np.int(np.mean(nonzerox[good_left_inds]))
        if len(good_right_inds) > minpix:        
            rightx_current = np.int(np.mean(nonzerox[good_right_inds]))

    # Concatenate the arrays of indices (previously was a list of lists of pixels)
    try:
        left_lane_inds = np.concatenate(left_lane_inds)
        right_lane_inds = np.concatenate(right_lane_inds)
    except ValueError:
        # Avoids an error if the above is not implemented fully
        pass

    # Extract left and right line pixel positions
    leftx = nonzerox[left_lane_inds]
    lefty = nonzeroy[left_lane_inds] 
    rightx = nonzerox[right_lane_inds]
    righty = nonzeroy[right_lane_inds]

    return leftx, lefty, rightx, righty, out_img


def fit_polynomial(binary_warped):
    """
    Find our lane pixels first
    """
    
    leftx, lefty, rightx, righty, out_img = find_lane_pixels(binary_warped)

    # Fit a second order polynomial to each using `np.polyfit`
    left_fit = np.polyfit(lefty, leftx, 2)
    right_fit = np.polyfit(righty, rightx, 2)

    # Generate x and y values for plotting
    ploty = np.linspace(0, binary_warped.shape[0]-1, binary_warped.shape[0] )
    try:
        left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
        right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
    except TypeError:
        # Avoids an error if `left` and `right_fit` are still none or incorrect
        print('The function failed to fit a line!')
        left_fitx = 1*ploty**2 + 1*ploty
        right_fitx = 1*ploty**2 + 1*ploty

    ## Visualization ##
    # Colors in the left and right lane regions
    out_img[lefty, leftx] = [255, 0, 0]
    out_img[righty, rightx] = [0, 0, 255]

    return out_img, left_fit, right_fit, ploty

Test Image

In [22]:
fname = './test_images/straight_lines1.jpg'    
fdir = './output_images/'

# Read the image
binary_warped = test_images[1]['top_down']

out_img, left_fit, right_fit, ploty = fit_polynomial(binary_warped)

left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]

# Plot the result
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(20, 10))
f.tight_layout()
ax1.imshow(binary_warped)
ax1.set_title('Binary Warped', fontsize=30)
#ax2.imshow(out_img, cmap='gray')
ax2.set_title('Polynomial Fit', fontsize=30)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)

ax2.plot(left_fitx, ploty, color='yellow', linewidth=10)
ax2.plot(right_fitx, ploty, color='yellow', linewidth=10)
ax2.imshow(out_img)

plt.savefig(fdir+'straight_lines1_polynomial_output.jpg')

Skip the sliding windows step once the lines are found

In [23]:
def fit_poly(img_shape, leftx, lefty, rightx, righty):
    """
    Fit a second order polynomial to each lane
    """
    
    left_fit = np.polyfit(lefty, leftx, 2)
    right_fit = np.polyfit(righty, rightx, 2)
    
    # Generate x and y values for plotting
    ploty = np.linspace(0, img_shape[0]-1, img_shape[0])
    
    # Calc both polynomials
    left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
    right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
    
    return left_fit, right_fit, left_fitx, right_fitx, ploty

def search_around_poly(binary_warped, left_fit, right_fit):
    # HYPERPARAMETER
    # Choose the width of the margin around the previous polynomial to search
    margin = 200

    # Grab activated pixels
    nonzero = binary_warped.nonzero()
    nonzeroy = np.array(nonzero[0])
    nonzerox = np.array(nonzero[1])

    
    # Set the area of search based on activated x-values 
    left_lane_inds = ((nonzerox > (left_fit[0]*(nonzeroy**2) + left_fit[1]*nonzeroy + 
                    left_fit[2] - margin)) & (nonzerox < (left_fit[0]*(nonzeroy**2) + 
                    left_fit[1]*nonzeroy + left_fit[2] + margin)))
    right_lane_inds = ((nonzerox > (right_fit[0]*(nonzeroy**2) + right_fit[1]*nonzeroy + 
                    right_fit[2] - margin)) & (nonzerox < (right_fit[0]*(nonzeroy**2) + 
                    right_fit[1]*nonzeroy + right_fit[2] + margin)))
    
    # Extract left and right line pixel positions
    leftx = nonzerox[left_lane_inds]
    lefty = nonzeroy[left_lane_inds] 
    rightx = nonzerox[right_lane_inds]
    righty = nonzeroy[right_lane_inds]
    
    # Fit new polynomials
    left_fit, right_fit, left_fitx, right_fitx, ploty = fit_poly(binary_warped.shape, leftx, lefty, rightx, righty)
    
    ## Visualization ##
    # Create an image to draw on and an image to show the selection window
    out_img = np.dstack((binary_warped, binary_warped, binary_warped))*255
    window_img = np.zeros_like(out_img)
    
    # Color in left and right line pixels
    out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
    out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]

    # Generate a polygon to illustrate the search window area
    left_line_window1 = np.array([np.transpose(np.vstack([left_fitx-margin, ploty]))])
    left_line_window2 = np.array([np.flipud(np.transpose(np.vstack([left_fitx+margin, 
                              ploty])))])
    left_line_pts = np.hstack((left_line_window1, left_line_window2))
    right_line_window1 = np.array([np.transpose(np.vstack([right_fitx-margin, ploty]))])
    right_line_window2 = np.array([np.flipud(np.transpose(np.vstack([right_fitx+margin, 
                              ploty])))])
    right_line_pts = np.hstack((right_line_window1, right_line_window2))

    # Draw the lane onto the warped blank image
    cv2.fillPoly(window_img, np.int_([left_line_pts]), (0,255, 0))
    cv2.fillPoly(window_img, np.int_([right_line_pts]), (0,255, 0))
    result = cv2.addWeighted(out_img, 1, window_img, 0.3, 0)
    
    return result, left_fit, right_fit, ploty
In [24]:
test_images[3]['top_down']
Out[24]:
array([[1, 1, 1, ..., 0, 0, 0],
       [1, 1, 1, ..., 0, 0, 0],
       [1, 1, 1, ..., 0, 0, 0],
       ...,
       [0, 0, 0, ..., 0, 0, 0],
       [0, 0, 0, ..., 0, 0, 0],
       [0, 0, 0, ..., 0, 0, 0]], dtype=uint8)
In [25]:
# Test on a sample images
binary_warped = test_images[4]['top_down']

# Polynomial fit values from the previous frame
left_fit = np.array([ 2.13935315e-04, -3.77507980e-01,  4.76902175e+02])
right_fit = np.array([4.17622148e-04, -4.93848953e-01,  1.11806170e+03])

ploty = np.linspace(0, binary_warped.shape[0]-1, binary_warped.shape[0])

left_fitx_prev = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx_prev = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]

# Run image through the pipeline
# Note that in your project, you'll also want to feed in the previous fits
result, left_fit, right_fit, ploty = search_around_poly(binary_warped, left_fit, right_fit)


left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]

# Visualize the resulting histogram
fig, ax = plt.subplots(figsize=(20, 10))
plt.plot(left_fitx_prev, ploty, color='red')
plt.plot(right_fitx_prev, ploty, color='red')
plt.plot(left_fitx, ploty, color='yellow')
plt.plot(right_fitx, ploty, color='yellow')
ax.imshow(result)
Out[25]:
<matplotlib.image.AxesImage at 0x1262c4510>

6 . Determine the Curvature of the Lane and Vehicle Position with Respect to Center

In [26]:
def measure_curvature_real(left_fit_cr, right_fit_cr, y_eval):
    '''
    Calculates the curvature of polynomial functions in meters.
    '''
    # Define conversions in x and y from pixels space to meters
    ym_per_pix = 30/720 # meters per pixel in y dimension
    xm_per_pix = 3.7/700 # meters per pixel in x dimension
        
    # Calculation of R_curve (radius of curvature)
    if left_fit_cr[0] != 0:
        left_curverad = ((1 + (2*left_fit_cr[0]*y_eval*ym_per_pix + left_fit_cr[1])**2)**1.5) / np.absolute(2*left_fit_cr[0])
    else: 
        left_curverad = 1000000
    if right_fit_cr[0] !=0:
        right_curverad = ((1 + (2*right_fit_cr[0]*y_eval*ym_per_pix + right_fit_cr[1])**2)**1.5) / np.absolute(2*right_fit_cr[0])
    else: 
        right_curverad = 1000000
    
    return left_curverad, right_curverad

def measure_distance_to_center_real(left_fit_cr, right_fit_cr, image_shape):
    '''
    Calculates the distance to center of the lane in meters. 
    '''
    # Define conversions in x and y from pixels space to meters
    ym_per_pix = 30/720 # meters per pixel in y dimension
    xm_per_pix = 3.7/700 # meters per pixel in x dimension

    y_eval = image_shape[0]
    
    left_x_eval = left_fit_cr[0]*y_eval**2 + left_fit_cr[1]*y_eval + left_fit_cr[2]
    right_x_eval = right_fit_cr[0]*y_eval**2 + right_fit_cr[1]*y_eval + right_fit_cr[2]

    lane_center_position = (right_x_eval + left_x_eval) /2
    image_center_position =  image_shape[1] / 2
    
    return (lane_center_position - image_center_position) * xm_per_pix

def measure_line_distance_to_center_real(line_fit_cr, m_per_pix, image_shape):
    '''
    Calculates the distance from line to center of the image in meters. 
    '''
    y_eval = image_shape[0]
    
    line_x_eval = line_fit_cr[0]*y_eval**2 + line_fit_cr[1]*y_eval + line_fit_cr[2]

    image_center_position =  image_shape[1] / 2
    
    return (line_x_eval - image_center_position) * m_per_pix

7. Process an Image

In [27]:
def draw_lanes_on_undistorted(image, top_down, left_fit, right_fit, ploty):
    """
    Draw lanes on the image
    """
    
    zeros = np.zeros_like(top_down).astype(np.uint8)
    lane_mask = np.dstack((zeros, zeros, zeros))

    left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
    right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
    
    l_line_pts = np.array([np.transpose(np.vstack([left_fitx, ploty]))])
    r_line_pts = np.array([np.flipud(np.transpose(np.vstack([right_fitx, ploty])))])
    pts = np.hstack((l_line_pts, r_line_pts))

    cv2.fillPoly(lane_mask, np.int_([pts]), (50,255,50))
    cv2.polylines(lane_mask, np.int32([l_line_pts]), isClosed=False, color=(50,50,255), thickness=20)
    cv2.polylines(lane_mask, np.int32([r_line_pts]), isClosed=False, color=(255,76,76), thickness=20)

    img_size = (image.shape[1], image.shape[0])

    lane_mask_unwarped = cv2.warpPerspective(lane_mask, Minv, img_size)
    
    result = cv2.addWeighted(image, 1, lane_mask_unwarped, 0.5, 0)

    return result
In [28]:
# Define a class to receive the characteristics of each line detection
class Line():
    def __init__(self):
       # was the line detected in the last iteration?
        self.detected = False  
        # polynomial coefficients averaged and low-pass filtered over frames
        self.best_fit = None  
        # polynomial coefficients for the most recent fit
        self.current_fit = None  
        # radius of curvature of the line in meters unit
        self.radius_of_curvature = None 
        # distance in meters of vehicle center from the line
        self.line_base_pos = None 
        # number of consecutive bad frames
        self.reset_counter = 0
        
    def reset(self):
        self.detected = False  
        self.current_fit = None  
        self.radius_of_curvature = None 
        self.line_base_pos = None 
        self.reset_counter = 0


class Boundaries():
    def __init__(self, left_line, right_line):
        self.right = left_line
        self.left = right_line
        curve_radius = None
        distance_to_center = None
        self.ploty = None
    
    def update(self, top_down_image):

        # Fit right and left line polynomials
        if self.left.detected or self.right.detected:
            result, left_fit_new, right_fit_new, ploty = search_around_poly(top_down_image, self.left.best_fit, self.right.best_fit)
            self.ploty = ploty
        else:
            result, left_fit_new, right_fit_new, ploty = fit_polynomial(top_down_image)
            self.ploty = ploty
        
        if len(left_fit_new) == 0:
            self.left.detected = False
            self.left.current_fit = self.left.best_fit
            left_fit_new = self.left.best_fit
            # restart after 10 consecutive bad frames
            if self.left.reset_counter == 10:
                self.left.reset()                

        if len(right_fit_new) == 0:
            self.right.detected = False
            self.right.current_fit = self.right.best_fit
            right_fit_new = self.right.best_fit
            # restart after 10 consecutive bad frames
            if self.right.reset_counter == 10:
                self.right.reset()                
            
        # The curvature of the lane 
        left_curve, right_curve = measure_curvature_real(left_fit_new, right_fit_new, top_down_image.shape[0])

        # Vehicle position with respect to center
        left_base_pos = measure_line_distance_to_center_real(left_fit_new, 3.7/700, top_down_image.shape)
        right_base_pos = measure_line_distance_to_center_real(right_fit_new, 3.7/700, top_down_image.shape)

        distance_to_center = measure_distance_to_center_real(left_fit_new, right_fit_new, top_down.shape)
        curve_radius = (left_curve + right_curve)/2
        
        # Update best fits if lines pass our criteria
        if (self.check_curvature(left_curve, right_curve, 3000) and self.check_separation(left_base_pos, right_base_pos, 3) and self.check_slope(left_fit_new, right_fit_new, top_down_image.shape[0], 1)) or ((self.left.best_fit is None) or (self.right.best_fit is None)):
                        
            self.left.current_fit = left_fit_new
            self.right.current_fit = right_fit_new
            
            if self.left.best_fit is not None:
                self.left.best_fit = list(np.round(np.array(self.left.current_fit) * 0.1 + np.array(self.left.best_fit) * 0.9 , decimals=4))
            else: 
                self.left.best_fit = self.left.current_fit
                
            if self.right.best_fit is not None:
                self.right.best_fit = list(np.round(np.array(self.right.current_fit) * 0.1 + np.array(self.right.best_fit) * 0.9 , decimals=4))
            else: 
                self.right.best_fit = self.right.current_fit
                            
            # Update curvature
            self.left.radius_of_curvature = left_curve
            self.right.radius_of_curvature = right_curve
        
            # Update vehicle position
            self.left.line_base_pos = left_base_pos
            self.right.line_base_pos = right_base_pos
        
            self.distance_to_center = distance_to_center
            self.curve_radius = curve_radius

            self.left.detected = True
            self.right.detected = True
            
            self.reset_counter = 0
            
        else:
            self.left.detected = False
            self.right.detected = False
            
            self.left.reset_counter += 1
            # restart after 10 consecutive bad frames
            if self.left.reset_counter == 10:
                self.left.reset()                

            self.right.reset_counter += 1
            # restart after 10 consecutive bad frames
            if self.right.reset_counter == 10:
                self.right.reset()                
        
    def check_curvature(self, curve1, curve2, threshold):
        similar_curvatures = False
        if np.absolute(curve1 - curve2) < threshold:
            similar_curvatures = True
        return similar_curvatures
            
    def check_separation(self, dist1, dist2, threshold):
        separated_by_distance = False
        if np.absolute(dist1 - dist2) > threshold:
            separated_by_distance = True
        return separated_by_distance

    def check_slope(self, left_line, right_line, y_eval, threshold):
        left_derivative = 2 * left_line[0]*y_eval + left_line[1]
        right_derivative = 2 * right_line[0]*y_eval + right_line[1]

        similar_slopes = False
        if np.absolute(left_derivative - right_derivative) < threshold:
            similar_slopes = True
        return similar_slopes
In [29]:
def process_image(image):
    
    """
    Complete process of one BGR image
    """
    
    #global left_fit, right_fit, ploty
    global left_fit, right_fit, boundaries
    
    img = cv2.cvtColor(image, cv2.COLOR_BGR2RGB)
           
    # Undistort the image
    undist = cv2.undistort(img, mtx, dist, None, mtx)
    undist_copy = undist.copy()

    # Threshold
    binary_image = thresholding_pipeline(undist)
        
    # Unwarp the image
    left_bottom = (185, 720)
    left_top = (585, 455)
    right_bottom = (1125, 720)
    right_top = (695, 455)
    src = np.float32([left_top, right_top, right_bottom, left_bottom])

    offset = 200
    height, width = binary_image.shape
    dst = np.float32([(offset, 0), (width-offset, 0), (width-offset, height), (offset, height)])

    top_down, M, Minv = unwarp(binary_image, src, dst)

    boundaries.update(top_down)
                
    # Warp the detected lane boundaries back onto the original image
    image_with_lane = draw_lanes_on_undistorted(image, top_down, left_fit.best_fit, right_fit.best_fit, boundaries.ploty)

    # Add curvature of the lane and distance from center on top of the image
    cv2.putText(image_with_lane, "Radius of Curvature: %s(m)" % int(boundaries.curve_radius), (100, 50), cv2.FONT_HERSHEY_DUPLEX, 1.5, [255, 255, 255], 2)
    if boundaries.distance_to_center > 0:
        cv2.putText(image_with_lane, "Vehicle is %.2fm left of center" % boundaries.distance_to_center, (100, 100), cv2.FONT_HERSHEY_DUPLEX, 1.5, [255, 255, 255], 2)
    else:
        cv2.putText(image_with_lane, "Vehicle is %.2fm right of center" % np.abs(boundaries.distance_to_center), (100, 100), cv2.FONT_HERSHEY_DUPLEX, 1.5, [255, 255, 255], 2)

    # The final image
    final_image = np.zeros((1080, 1280, 3), dtype=np.uint8)
    final_image[360:1080, 0:1280] = image_with_lane
    
    temp = np.dstack((binary_image, binary_image, binary_image)) * 255
    final_image[0:360, 0:640] = cv2.resize(temp, (640,360), interpolation=cv2.INTER_AREA) 

    temp = np.dstack((top_down, top_down, top_down)) * 255
    final_image[0:360, 640:1280] = cv2.resize(temp, (640,360), interpolation=cv2.INTER_AREA) 

    return final_image

Test Image

In [30]:
left_fit = Line()
right_fit = Line()
boundaries = Boundaries(left_fit, right_fit)

fname = './test_images/test4.jpg'    
fdir = './output_images/'

# Read the image
img = cv2.imread(fname)
img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)

# Run image through the pipeline
processed_image = process_image(img)

# Plot the result
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(20, 10))
f.tight_layout()
ax1.imshow(img)
ax1.set_title('Original Image', fontsize=30)
ax2.set_title('1) binary 2) top View 3) Lanes Overlaid', fontsize=30)
ax2.imshow(processed_image)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)

plt.savefig(fdir+'test4_pipeline_output.jpg')

8. Process a Video

In [31]:
# Import everything needed to edit/save/watch video clips
from moviepy.editor import VideoFileClip
from IPython.display import HTML

Standard Video

In [32]:
left_fit = Line()
right_fit = Line()
boundaries = Boundaries(left_fit, right_fit)

video_output = 'output_project_video.mp4'
clip = VideoFileClip('project_video.mp4')
video_clip = clip.fl_image(process_image)
%time video_clip.write_videofile(video_output, audio=False)

HTML("""
<video width="960" height="540" controls>
  <source src="{0}">
</video>
""".format(video_output))
t:   0%|          | 3/1260 [00:00<01:08, 18.26it/s, now=None]
Moviepy - Building video output_project_video.mp4.
Moviepy - Writing video output_project_video.mp4

                                                                
Moviepy - Done !
Moviepy - video ready output_project_video.mp4
CPU times: user 7min 1s, sys: 50.2 s, total: 7min 51s
Wall time: 2min 10s
Out[32]:

Challenge Video

In [33]:
left_fit = Line()
right_fit = Line()
boundaries = Boundaries(left_fit, right_fit)

video_output = 'output_challenge_video.mp4'
clip = VideoFileClip('challenge_video.mp4')
video_clip = clip.fl_image(process_image)
%time video_clip.write_videofile(video_output, audio=False)

HTML("""
<video width="960" height="540" controls>
  <source src="{0}">
</video>
""".format(video_output))
t:   0%|          | 2/485 [00:00<00:24, 19.71it/s, now=None]
Moviepy - Building video output_challenge_video.mp4.
Moviepy - Writing video output_challenge_video.mp4

                                                              
Moviepy - Done !
Moviepy - video ready output_challenge_video.mp4
CPU times: user 2min 29s, sys: 19.5 s, total: 2min 48s
Wall time: 45.6 s
Out[33]:

Harder Challenge

In [34]:
left_fit = Line()
right_fit = Line()
boundaries = Boundaries(left_fit, right_fit)

video_output = 'output_harder_challenge_video.mp4'
clip = VideoFileClip('harder_challenge_video.mp4')
video_clip = clip.fl_image(process_image)
%time video_clip.write_videofile(video_output, audio=False)

HTML("""
<video width="960" height="540" controls>
  <source src="{0}">
</video>
""".format(video_output))
t:   0%|          | 2/1199 [00:00<01:06, 18.02it/s, now=None]
Moviepy - Building video output_harder_challenge_video.mp4.
Moviepy - Writing video output_harder_challenge_video.mp4

                                                                
Moviepy - Done !
Moviepy - video ready output_harder_challenge_video.mp4
CPU times: user 7min 13s, sys: 49.3 s, total: 8min 2s
Wall time: 2min 11s
Out[34]: